{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:R3QKG5WETZC7TN3XPSMZQGTR4O","short_pith_number":"pith:R3QKG5WE","canonical_record":{"source":{"id":"2608.04694","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-08-05T11:01:13Z","cross_cats_sorted":[],"title_canon_sha256":"5ef6d9595330788a8821d832a10782588ff04e12bd6a06dd9ede79db830a42ad","abstract_canon_sha256":"24582121cff28905f174a12f1796b52c4e958ae613e743ab6c6a500b2419efa0"},"schema_version":"1.0"},"canonical_sha256":"8ee0a376c49e45f9b7777c99981a71e3be1d5895debb62777b8a098876932014","source":{"kind":"arxiv","id":"2608.04694","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.04694","created_at":"2026-08-06T01:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"2608.04694v1","created_at":"2026-08-06T01:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04694","created_at":"2026-08-06T01:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"R3QKG5WETZC7","created_at":"2026-08-06T01:46:31Z"},{"alias_kind":"pith_short_16","alias_value":"R3QKG5WETZC7TN3X","created_at":"2026-08-06T01:46:31Z"},{"alias_kind":"pith_short_8","alias_value":"R3QKG5WE","created_at":"2026-08-06T01:46:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:R3QKG5WETZC7TN3XPSMZQGTR4O","target":"record","payload":{"canonical_record":{"source":{"id":"2608.04694","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-08-05T11:01:13Z","cross_cats_sorted":[],"title_canon_sha256":"5ef6d9595330788a8821d832a10782588ff04e12bd6a06dd9ede79db830a42ad","abstract_canon_sha256":"24582121cff28905f174a12f1796b52c4e958ae613e743ab6c6a500b2419efa0"},"schema_version":"1.0"},"canonical_sha256":"8ee0a376c49e45f9b7777c99981a71e3be1d5895debb62777b8a098876932014","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-06T01:46:31.135528Z","signature_b64":"E6rxCuf8KkTU9UTKOkwvn+d780QjJ7VCiAPhtdnKw1vbbjx6ES5dRYhk/HHmAtBfev4eS4oPXikfT8artAaQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ee0a376c49e45f9b7777c99981a71e3be1d5895debb62777b8a098876932014","last_reissued_at":"2026-08-06T01:46:31.134103Z","signature_status":"signed_v1","first_computed_at":"2026-08-06T01:46:31.134103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.04694","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-06T01:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gicv6b8lXm8lBTrgAxZHQK6AounsAQ3SY/9OTKCYXq4c5utVhgGWUxVOya8sI+m2bdzulCnUJOn4O7EZut4XBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T13:32:35.550001Z"},"content_sha256":"50c1009c2d291ecfe2754cee2807ee165a8a33c56c84db318abc39b7b7d300ce","schema_version":"1.0","event_id":"sha256:50c1009c2d291ecfe2754cee2807ee165a8a33c56c84db318abc39b7b7d300ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:R3QKG5WETZC7TN3XPSMZQGTR4O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractal properties of the cosmic web","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Jaan Einasto","submitted_at":"2026-08-05T11:01:13Z","abstract_excerpt":"The cosmic web is one of the most complex systems in nature, consisting of galaxies and clusters of galaxies connected by filaments and walls, and separated by large empty regions known as cosmic voids. The most common method for describing the web is the correlation function and its derivative, the structure function and fractal dimension function. In this paper I review the fractal properties of the cosmic web within the concordance {\\Lambda}CDM framework. I describe how the fractal function is derived from the angular and spatial distributions of galaxies and discuss the relations between t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04694","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.04694/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-06T01:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hhVCn1WAPai+Mvt9kZDHMIjrmTBNguBouWV194etPjXJ6Wh/F4Tt3509SlfKCXcd4DabKB4p0/BRykM+ufR1BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T13:32:35.550901Z"},"content_sha256":"d42a49a83a7d0e6ce59e9eefca46041d6fe7901c94081f7de42a09f113dd1e48","schema_version":"1.0","event_id":"sha256:d42a49a83a7d0e6ce59e9eefca46041d6fe7901c94081f7de42a09f113dd1e48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R3QKG5WETZC7TN3XPSMZQGTR4O/bundle.json","state_url":"https://pith.science/pith/R3QKG5WETZC7TN3XPSMZQGTR4O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R3QKG5WETZC7TN3XPSMZQGTR4O/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T13:32:35Z","links":{"resolver":"https://pith.science/pith/R3QKG5WETZC7TN3XPSMZQGTR4O","bundle":"https://pith.science/pith/R3QKG5WETZC7TN3XPSMZQGTR4O/bundle.json","state":"https://pith.science/pith/R3QKG5WETZC7TN3XPSMZQGTR4O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R3QKG5WETZC7TN3XPSMZQGTR4O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:R3QKG5WETZC7TN3XPSMZQGTR4O","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"24582121cff28905f174a12f1796b52c4e958ae613e743ab6c6a500b2419efa0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-08-05T11:01:13Z","title_canon_sha256":"5ef6d9595330788a8821d832a10782588ff04e12bd6a06dd9ede79db830a42ad"},"schema_version":"1.0","source":{"id":"2608.04694","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.04694","created_at":"2026-08-06T01:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"2608.04694v1","created_at":"2026-08-06T01:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.04694","created_at":"2026-08-06T01:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"R3QKG5WETZC7","created_at":"2026-08-06T01:46:31Z"},{"alias_kind":"pith_short_16","alias_value":"R3QKG5WETZC7TN3X","created_at":"2026-08-06T01:46:31Z"},{"alias_kind":"pith_short_8","alias_value":"R3QKG5WE","created_at":"2026-08-06T01:46:31Z"}],"graph_snapshots":[{"event_id":"sha256:d42a49a83a7d0e6ce59e9eefca46041d6fe7901c94081f7de42a09f113dd1e48","target":"graph","created_at":"2026-08-06T01:46:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.04694/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The cosmic web is one of the most complex systems in nature, consisting of galaxies and clusters of galaxies connected by filaments and walls, and separated by large empty regions known as cosmic voids. The most common method for describing the web is the correlation function and its derivative, the structure function and fractal dimension function. In this paper I review the fractal properties of the cosmic web within the concordance {\\Lambda}CDM framework. I describe how the fractal function is derived from the angular and spatial distributions of galaxies and discuss the relations between t","authors_text":"Jaan Einasto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-08-05T11:01:13Z","title":"Fractal properties of the cosmic web"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.04694","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:50c1009c2d291ecfe2754cee2807ee165a8a33c56c84db318abc39b7b7d300ce","target":"record","created_at":"2026-08-06T01:46:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"24582121cff28905f174a12f1796b52c4e958ae613e743ab6c6a500b2419efa0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-08-05T11:01:13Z","title_canon_sha256":"5ef6d9595330788a8821d832a10782588ff04e12bd6a06dd9ede79db830a42ad"},"schema_version":"1.0","source":{"id":"2608.04694","kind":"arxiv","version":1}},"canonical_sha256":"8ee0a376c49e45f9b7777c99981a71e3be1d5895debb62777b8a098876932014","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ee0a376c49e45f9b7777c99981a71e3be1d5895debb62777b8a098876932014","first_computed_at":"2026-08-06T01:46:31.134103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-06T01:46:31.134103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E6rxCuf8KkTU9UTKOkwvn+d780QjJ7VCiAPhtdnKw1vbbjx6ES5dRYhk/HHmAtBfev4eS4oPXikfT8artAaQCw==","signature_status":"signed_v1","signed_at":"2026-08-06T01:46:31.135528Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.04694","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50c1009c2d291ecfe2754cee2807ee165a8a33c56c84db318abc39b7b7d300ce","sha256:d42a49a83a7d0e6ce59e9eefca46041d6fe7901c94081f7de42a09f113dd1e48"],"state_sha256":"815c72dc653e53c04c77095cab01182d0c0df2e7e413257201d9cdebe3502aa9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g4ETYSWuAkiUY+eUZ2SNRWC/4dpXBV0Zq8UKPK6JgkEP/ssw8HRHykpFcceQnNV3TAt72zEQyZ/QlcrtzKjFAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T13:32:35.620810Z","bundle_sha256":"12dc302b2a75f0f03537f7bebef87bf703b5b2df695c0074b2f879273a1227ae"}}